//  (C) Copyright John Maddock 2019.
//  Use, modification and distribution are subject to the
//  Boost Software License, Version 1.0. (See accompanying file
//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

// Contains Quickbook snippets used by boost/libs/multiprecision/doc/multiprecision.qbk,
// section Literal Types and constexpr Support.

#include <iostream>
#include <boost/config.hpp>

#ifdef BOOST_HAS_FLOAT128
#include <nil/crypto3/multiprecision/float128.hpp>
#endif

//[constexpr_circle
#include <boost/math/constants/constants.hpp>    // For constant pi with full precision of type T.
// using  boost::math::constants::pi;

template<class T>
inline constexpr T circumference(T radius) {
    return 2 * boost::math::constants::pi<T>() * radius;
}

template<class T>
inline constexpr T area(T radius) {
    return boost::math::constants::pi<T>() * radius * radius;
}
//] [/constexpr_circle]

template<class T, unsigned Order>
struct const_polynomial {
public:
    T data[Order + 1];

public:
    constexpr const_polynomial(T val = 0) : data {val} {
    }
    constexpr const_polynomial(const std::initializer_list<T>& init) : data {} {
        if (init.size() > Order + 1)
            throw std::range_error("Too many initializers in list!");
        for (unsigned i = 0; i < init.size(); ++i)
            data[i] = init.begin()[i];
    }
    constexpr T& operator[](std::size_t N) {
        return data[N];
    }
    constexpr const T& operator[](std::size_t N) const {
        return data[N];
    }
    template<class U>
    constexpr T operator()(U val) const {
        T result = data[Order];
        for (unsigned i = Order; i > 0; --i) {
            result *= val;
            result += data[i - 1];
        }
        return result;
    }
    constexpr const_polynomial<T, Order - 1> derivative() const {
        const_polynomial<T, Order - 1> result;
        for (unsigned i = 1; i <= Order; ++i) {
            result[i - 1] = (*this)[i] * i;
        }
        return result;
    }
    constexpr const_polynomial operator-() {
        const_polynomial t(*this);
        for (unsigned i = 0; i <= Order; ++i)
            t[i] = -t[i];
        return t;
    }
    template<class U>
    constexpr const_polynomial& operator*=(U val) {
        for (unsigned i = 0; i <= Order; ++i)
            data[i] = data[i] * val;
        return *this;
    }
    template<class U>
    constexpr const_polynomial& operator/=(U val) {
        for (unsigned i = 0; i <= Order; ++i)
            data[i] = data[i] / val;
        return *this;
    }
    template<class U>
    constexpr const_polynomial& operator+=(U val) {
        data[0] += val;
        return *this;
    }
    template<class U>
    constexpr const_polynomial& operator-=(U val) {
        data[0] -= val;
        return *this;
    }
};

template<class T, unsigned Order1, unsigned Order2>
inline constexpr const_polynomial<T, (Order1 > Order2 ? Order1 : Order2)>
    operator+(const const_polynomial<T, Order1>& a, const const_polynomial<T, Order2>& b) {
    if constexpr (Order1 > Order2) {
        const_polynomial<T, Order1> result(a);
        for (unsigned i = 0; i <= Order2; ++i)
            result[i] += b[i];
        return result;
    } else {
        const_polynomial<T, Order2> result(b);
        for (unsigned i = 0; i <= Order1; ++i)
            result[i] += a[i];
        return result;
    }
}
template<class T, unsigned Order1, unsigned Order2>
inline constexpr const_polynomial<T, (Order1 > Order2 ? Order1 : Order2)>
    operator-(const const_polynomial<T, Order1>& a, const const_polynomial<T, Order2>& b) {
    if constexpr (Order1 > Order2) {
        const_polynomial<T, Order1> result(a);
        for (unsigned i = 0; i <= Order2; ++i)
            result[i] -= b[i];
        return result;
    } else {
        const_polynomial<T, Order2> result(b);
        for (unsigned i = 0; i <= Order1; ++i)
            result[i] = a[i] - b[i];
        return result;
    }
}
template<class T, unsigned Order1, unsigned Order2>
inline constexpr const_polynomial<T, Order1 + Order2> operator*(const const_polynomial<T, Order1>& a,
                                                                const const_polynomial<T, Order2>& b) {
    const_polynomial<T, Order1 + Order2> result;
    for (unsigned i = 0; i <= Order1; ++i) {
        for (unsigned j = 0; j <= Order2; ++j) {
            result[i + j] += a[i] * b[j];
        }
    }
    return result;
}
template<class T, unsigned Order, class U>
inline constexpr const_polynomial<T, Order> operator*(const const_polynomial<T, Order>& a, const U& b) {
    const_polynomial<T, Order> result(a);
    for (unsigned i = 0; i <= Order; ++i) {
        result[i] *= b;
    }
    return result;
}
template<class U, class T, unsigned Order>
inline constexpr const_polynomial<T, Order> operator*(const U& b, const const_polynomial<T, Order>& a) {
    const_polynomial<T, Order> result(a);
    for (unsigned i = 0; i <= Order; ++i) {
        result[i] *= b;
    }
    return result;
}
template<class T, unsigned Order, class U>
inline constexpr const_polynomial<T, Order> operator/(const const_polynomial<T, Order>& a, const U& b) {
    const_polynomial<T, Order> result;
    for (unsigned i = 0; i <= Order; ++i) {
        result[i] /= b;
    }
    return result;
}

//[hermite_example
template<class T, unsigned Order>
class hermite_polynomial {
    const_polynomial<T, Order> m_data;

public:
    constexpr hermite_polynomial() :
        m_data(hermite_polynomial<T, Order - 1>().data() * const_polynomial<T, 1> {0, 2} -
               hermite_polynomial<T, Order - 1>().data().derivative()) {
    }
    constexpr const const_polynomial<T, Order>& data() const {
        return m_data;
    }
    constexpr const T& operator[](std::size_t N) const {
        return m_data[N];
    }
    template<class U>
    constexpr T operator()(U val) const {
        return m_data(val);
    }
};
//] [/hermite_example]

//[hermite_example2
template<class T>
class hermite_polynomial<T, 0> {
    const_polynomial<T, 0> m_data;

public:
    constexpr hermite_polynomial() : m_data {1} {
    }
    constexpr const const_polynomial<T, 0>& data() const {
        return m_data;
    }
    constexpr const T& operator[](std::size_t N) const {
        return m_data[N];
    }
    template<class U>
    constexpr T operator()(U val) {
        return m_data(val);
    }
};

template<class T>
class hermite_polynomial<T, 1> {
    const_polynomial<T, 1> m_data;

public:
    constexpr hermite_polynomial() : m_data {0, 2} {
    }
    constexpr const const_polynomial<T, 1>& data() const {
        return m_data;
    }
    constexpr const T& operator[](std::size_t N) const {
        return m_data[N];
    }
    template<class U>
    constexpr T operator()(U val) {
        return m_data(val);
    }
};
//] [/hermite_example2]

void test_double() {
    constexpr double radius = 2.25;
    constexpr double c = circumference(radius);
    constexpr double a = area(radius);

    std::cout << "Circumference = " << c << std::endl;
    std::cout << "Area = " << a << std::endl;

    constexpr const_polynomial<double, 2> pa = {3, 4};
    constexpr const_polynomial<double, 2> pb = {5, 6};
    static_assert(pa[0] == 3);
    static_assert(pa[1] == 4);
    constexpr auto pc = pa * 2;
    static_assert(pc[0] == 6);
    static_assert(pc[1] == 8);
    constexpr auto pd = 3 * pa;
    static_assert(pd[0] == 3 * 3);
    static_assert(pd[1] == 4 * 3);
    constexpr auto pe = pa + pb;
    static_assert(pe[0] == 3 + 5);
    static_assert(pe[1] == 4 + 6);
    constexpr auto pf = pa - pb;
    static_assert(pf[0] == 3 - 5);
    static_assert(pf[1] == 4 - 6);
    constexpr auto pg = pa * pb;
    static_assert(pg[0] == 15);
    static_assert(pg[1] == 38);
    static_assert(pg[2] == 24);

    constexpr hermite_polynomial<double, 2> h1;
    static_assert(h1[0] == -2);
    static_assert(h1[1] == 0);
    static_assert(h1[2] == 4);

    constexpr hermite_polynomial<double, 3> h3;
    static_assert(h3[0] == 0);
    static_assert(h3[1] == -12);
    static_assert(h3[2] == 0);
    static_assert(h3[3] == 8);

    constexpr hermite_polynomial<double, 9> h9;
    static_assert(h9[0] == 0);
    static_assert(h9[1] == 30240);
    static_assert(h9[2] == 0);
    static_assert(h9[3] == -80640);
    static_assert(h9[4] == 0);
    static_assert(h9[5] == 48384);
    static_assert(h9[6] == 0);
    static_assert(h9[7] == -9216);
    static_assert(h9[8] == 0);
    static_assert(h9[9] == 512);

    static_assert(h9(0.5) == 6481);
}

void test_float128() {
#ifdef BOOST_HAS_FLOAT128
    //[constexpr_circle_usage

    using nil::crypto3::multiprecision::float128;

    constexpr float128 radius = 2.25;
    constexpr float128 c = circumference(radius);
    constexpr float128 a = area(radius);

    std::cout << "Circumference = " << c << std::endl;
    std::cout << "Area = " << a << std::endl;

    //]   [/constexpr_circle_usage]

    constexpr hermite_polynomial<float128, 2> h1;
    static_assert(h1[0] == -2);
    static_assert(h1[1] == 0);
    static_assert(h1[2] == 4);

    constexpr hermite_polynomial<float128, 3> h3;
    static_assert(h3[0] == 0);
    static_assert(h3[1] == -12);
    static_assert(h3[2] == 0);
    static_assert(h3[3] == 8);

    //[hermite_example3
    constexpr hermite_polynomial<float128, 9> h9;
    //
    // Verify that the polynomial's coefficients match the known values:
    //
    static_assert(h9[0] == 0);
    static_assert(h9[1] == 30240);
    static_assert(h9[2] == 0);
    static_assert(h9[3] == -80640);
    static_assert(h9[4] == 0);
    static_assert(h9[5] == 48384);
    static_assert(h9[6] == 0);
    static_assert(h9[7] == -9216);
    static_assert(h9[8] == 0);
    static_assert(h9[9] == 512);
    //
    // Define an abscissa value to evaluate at:
    constexpr float128 abscissa(0.5);
    //
    // Evaluate H_9(0.5) using all constexpr arithmetic, and check that it has the expected result:
    static_assert(h9(abscissa) == 6481);
    //]
#endif
}

int main() {
    test_double();
    test_float128();
    std::cout << "Done!" << std::endl;
}
